Table of Contents

A Web Server for Zoomable Chaos Game Represenations

Quick Demo

Overview

Chaos Game Representation

Chaos Game Representation (CGR) is a generalized scale-independent Markov probability table for the sequence, and oligomer tables (see document for "kmer_table" function) can be deduced from CGR image.

CGR is generated by the following procedure:

Start from position (0,0) or the origin of two dimensional coordinate.

Four nucleotides are located at the four corners:
A: (-1, 1) upper left
T: (1, -1) lower right
G: (1, 1) upper right
C: (-1, -1) lower left

For each nucleotide (in reverse order to match k-mer table; i.e., match forward Markov chain), move and mark the new location which is halfway between the current location and the nucleotide. For example, if the last letter is T, position is moved from (0,0) to midpoint between (1, -1) and (0,0), which is (0.5, -0.5).

Repeat this procedure for all nucleotides.

k-mer table

This program creates an image showing the abundance of all k-mers (oligonucleotides of length k) in a given sequence. For example, for tetramers (k=4), resulting image is composed of 4^4 = 256 boxes, each representing an oligomer. Oligomer name and abundance is written within these boxes, and abundance is also visualized with the box color, from white (none) to black (highly frequent).

This k-mer table is alternatively known as the FCGR (frequency matrices extracted from Chaos Game Representation).

Position of the oligomers can be recursively located as follows:

For each letter in an oligomer, a box is subdivided into four quadrants, where A is upper left, T is lower right, G is upper right, and C is lower left. Therefore, oligomer ACGT is in the

A = upper left quadrant
C = lower left within the above quadrant
G = upper right within the above quadrant
T = lower right within the above quadrant

Zoomable Google Maps

For CGR and k-mer tables to be useful as generalized scale-independent Markov probability table, it is critical for a user to be able to locate the oligonucleotides of interest quickly within the complex image. For this purpose, we have implemented CGR as zoomable Google Maps.

Here you can easily pan and zoom the large image with the same user interface as the familiar Google Maps; therefore, you can use the controller located in the top left corner for panning and zooming, or double clicking or use mouse scroll wheel for zooming, and so on.

As an addition, we have implemented a search capability. The search box is located at the top center of the map, where you can type in oligonucleotide sequences to perform incremental search/highlight over the map. For example, typing "CG" in the search box immediately highlights the position of oligomers starting with letters "CG".

You can use "N" to represent wild card nucleotide. Therefore, searching for "NCG" highlights four regions corresponding to "ACG", "TCG", "GCG", and "CCG". With this feature, users can quickly locate the oligonucleotide of interest, and observe the Markov chain probabilities following the specified nucleotides.

Chaos Game Representation for five prokaryotes

Click on the images to enlarge.

Escherichia coli

Bacillus subtilis

Mycoplasma genitalium

Synechococcus sp.

Pyrococcus furiosus

Usage

Web Service (Generation of images)

Basically, our web service can be accessed by specifying the URL according to a certain syntax.

Syntax:

http://rest.g-language.org/[genome]/[method]/

Here the [genome] is a RefSeq accession number (see here for listing), and [method] is either cgr (for Chaos Game Representation) or kmer_table (for k-mer table).

In this way, all maps are generated on the fly, and is always up-to-date. Moreover, other web-pages or web-database sites can utilize our service to add CGR and k-mer table to their website, by simply referring to our URL.

To use with your own sequence data (i.e. those not included in our list of genomes, access the following URL and upload.

In order to change the parameters, such as the length of oligomers for kmer_table (-k option), generation of Google Map (-gmap⇒1 option), or changing the image width for cgr (-width option), simply add these options and values to the function call, as follows: